Last week I wrote a short paper on an idea recently put forth by Farrah et al., that claimed that black holes may be the source of dark energy. The idea is basically the following: if black holes are coupled to the expansion of the universe, then certain black hole theories predict that they may grow with with the scale factor of the universe. In other words, as the Universe grows, every black hole should grow as well, and the offset in that mass increase can power the expansion of the Universe (loosely speaking). For this to work though, black holes would have to grow at an extreme rate, roughly proportional to (1+z)^3
This, however, is inconsistent with the masses and ages of black holes in globular clusters, in particular the 2 (or probably 3) black holes in NGC 3201. There, we have measured M sin (i) masses of 4.5, 7.7 and (probably) 4.4 solar masses. Given the age of the cluster, these black holes would have had to grow by a factor of nearly 55 from it’s formation at redshift 2.8 to the present day. Assuming that the black holes had to be born above the mass of the largest neutron stars, the *only* way this could work is if both (or all three) black holes are essentially face on to us. The odds of that are a simple probability argument, and aren’t great:
Essentially, even if I assume very generous errors on the cluster age (-3 sigma), consider only the two reliable black hole candidates, and give them a very generous (+3 sigma) error as well, the odds of them being face on enough for both black holes to be born above 2.2 solar masses is about 10^-4. If I assume the median measurements instead and throw in the 3rd black hole (which has a 82% chance of being a black hole, see the discussion in section 7.3 of Giesers et al., 2019), then this probability goes down to 10^-9.
In other words, unless nature is seriously conspiring against us, black holes have not grown enough to explain the origin of dark energy